Question

Find theta for which sin theta = cos theta If theta is greater than 180 degree but less than 360 degree

Answer 1

SOLUTION

TO DETERMINE

$\sf{The \: value \: of \: \: \theta }$ When

$\sf{ \sin \theta = \cos \theta \: \: \: \: and \: \: \: {180}^{ \circ} < \theta < {360}^{ \circ} } \:$

EVALUATION

Here it is given that

$\sf{ \sin \theta = \cos \theta \: \: \: \: and \: \: \: {180}^{ \circ} < \theta < {360}^{ \circ} } \:$

Now

$\sf{ \sin \theta = \cos \theta \: \: \: \: \: gives} \:$

$\tan \theta \: = 1$

$\implies \: \tan \theta \: = \tan \: {45}^{ \circ}$

$\implies \: \tan \theta \: = \tan \: ( {180}^{ \circ} + {45}^{ \circ} )$

$\implies \: \tan \theta \: = \tan \: {225}^{ \circ}$

$\implies \: \theta \: = \: {225}^{ \circ}$

FINAL ANSWER

Hence the required value of $\theta$ is 225°

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Answer 2

Step-by-step explanation:

Thevalueofθ When

\sf{ \sin \theta = \cos \theta \: \: \: \: and \: \: \: {180}^{ \circ} < \theta < {360}^{ \circ} } \:sinθ=cosθand180

∘

<θ<360

∘

EVALUATION

Here it is given that

\sf{ \sin \theta = \cos \theta \: \: \: \: and \: \: \: {180}^{ \circ} < \theta < {360}^{ \circ} } \:sinθ=cosθand180

∘

<θ<360

∘

Now

\sf{ \sin \theta = \cos \theta \: \: \: \: \: gives} \:sinθ=cosθgives

\tan \theta \: = 1tanθ=1

\implies \: \tan \theta \: = \tan \: {45}^{ \circ}⟹tanθ=tan45

∘

\implies \: \tan \theta \: = \tan \: ( {180}^{ \circ} + {45}^{ \circ} )⟹tanθ=tan(180

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+45

∘

)

\implies \: \tan \theta \: = \tan \: {225}^{ \circ}⟹tanθ=tan225

∘

\implies \: \theta \: = \: {225}^{ \circ}⟹θ=225

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